{"id":"https://openalex.org/W4224948589","doi":"https://doi.org/10.1109/tpami.2022.3172214","title":"Hybrid ISTA: Unfolding ISTA With Convergence Guarantees Using Free-Form Deep Neural Networks","display_name":"Hybrid ISTA: Unfolding ISTA With Convergence Guarantees Using Free-Form Deep Neural Networks","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4224948589","doi":"https://doi.org/10.1109/tpami.2022.3172214","pmid":"https://pubmed.ncbi.nlm.nih.gov/35503824"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2022.3172214","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3172214","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2204.11640","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073652872","display_name":"Ziyang Zheng","orcid":"https://orcid.org/0000-0001-9923-8016"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ziyang Zheng","raw_affiliation_strings":["Department of Electronic Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045342512","display_name":"Wenrui Dai","orcid":"https://orcid.org/0000-0003-2522-5778"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenrui Dai","raw_affiliation_strings":["Department of Computer Science and Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China, 200240"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China, 200240","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086442836","display_name":"Duoduo Xue","orcid":"https://orcid.org/0000-0002-6608-5700"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Duoduo Xue","raw_affiliation_strings":["Department of Electronic Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100675587","display_name":"Chenglin Li","orcid":"https://orcid.org/0000-0003-2888-594X"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenglin Li","raw_affiliation_strings":["Department of Electronic Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016006337","display_name":"Junni Zou","orcid":"https://orcid.org/0000-0002-9694-9880"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junni Zou","raw_affiliation_strings":["Department of Computer Science and Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002494284","display_name":"Hongkai Xiong","orcid":"https://orcid.org/0000-0003-4552-0029"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongkai Xiong","raw_affiliation_strings":["Electronic Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electronic Engineering, Shanghai Jiao Tong University, 12474 Shanghai, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5073652872"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":3.8175,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.94231528,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"3","first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6516772508621216},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6157767176628113},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5535424947738647},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5476119518280029},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5324951410293579},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.521898090839386},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.47809168696403503},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40653109550476074},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3351072669029236},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3110979199409485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24793654680252075}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6516772508621216},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6157767176628113},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5535424947738647},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5476119518280029},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5324951410293579},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.521898090839386},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.47809168696403503},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40653109550476074},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3351072669029236},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3110979199409485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24793654680252075},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tpami.2022.3172214","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3172214","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:35503824","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35503824","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null},{"id":"pmh:oai:arXiv.org:2204.11640","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.11640","pdf_url":"https://arxiv.org/pdf/2204.11640","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2204.11640","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.11640","pdf_url":"https://arxiv.org/pdf/2204.11640","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3425091141","display_name":null,"funder_award_id":"61871267","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3438946646","display_name":null,"funder_award_id":"61932022","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3628871441","display_name":null,"funder_award_id":"61720106001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4936292138","display_name":null,"funder_award_id":"T2122024","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G510744082","display_name":null,"funder_award_id":"61831018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5326461368","display_name":null,"funder_award_id":"61971285","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6094063813","display_name":null,"funder_award_id":"62125109","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6393920532","display_name":null,"funder_award_id":"61972256","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7123918047","display_name":null,"funder_award_id":"62120106007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8700549466","display_name":null,"funder_award_id":"61931023","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W1512208174","https://openalex.org/W1519983590","https://openalex.org/W1540764732","https://openalex.org/W1901129140","https://openalex.org/W1977520307","https://openalex.org/W1980454827","https://openalex.org/W1986737463","https://openalex.org/W2004160833","https://openalex.org/W2005876975","https://openalex.org/W2027982384","https://openalex.org/W2056636001","https://openalex.org/W2063978378","https://openalex.org/W2076541487","https://openalex.org/W2082029531","https://openalex.org/W2100556411","https://openalex.org/W2112447569","https://openalex.org/W2119667497","https://openalex.org/W2121927366","https://openalex.org/W2129131372","https://openalex.org/W2135046866","https://openalex.org/W2136885855","https://openalex.org/W2160979406","https://openalex.org/W2164278908","https://openalex.org/W2185175083","https://openalex.org/W2194775991","https://openalex.org/W2273561594","https://openalex.org/W2289917018","https://openalex.org/W2590877996","https://openalex.org/W2605819213","https://openalex.org/W2619204584","https://openalex.org/W2766452532","https://openalex.org/W2798559986","https://openalex.org/W2902719825","https://openalex.org/W2962975464","https://openalex.org/W2963297739","https://openalex.org/W2963446712","https://openalex.org/W2963590174","https://openalex.org/W2963837252","https://openalex.org/W2964010455","https://openalex.org/W2969478734","https://openalex.org/W3098745759","https://openalex.org/W3101710822","https://openalex.org/W3175662981","https://openalex.org/W4293581666","https://openalex.org/W4296234188","https://openalex.org/W6631077220","https://openalex.org/W6631190155","https://openalex.org/W6638667902","https://openalex.org/W6676727762","https://openalex.org/W6686534882","https://openalex.org/W6704584212","https://openalex.org/W6704980600","https://openalex.org/W6729455701","https://openalex.org/W6729956949","https://openalex.org/W6730222102","https://openalex.org/W6739495466","https://openalex.org/W6739675538","https://openalex.org/W6748028286","https://openalex.org/W6751955427","https://openalex.org/W6754103055","https://openalex.org/W6757612955","https://openalex.org/W6762973898","https://openalex.org/W6767423860","https://openalex.org/W6771692809","https://openalex.org/W6780226713","https://openalex.org/W6784333009"],"related_works":["https://openalex.org/W1517908938","https://openalex.org/W4317939968","https://openalex.org/W2281834912","https://openalex.org/W1489941249","https://openalex.org/W4390144857","https://openalex.org/W3123492739","https://openalex.org/W4320486059","https://openalex.org/W2494168571","https://openalex.org/W2033096984","https://openalex.org/W3121191496"],"abstract_inverted_index":{"It":[0],"is":[1,108,138,156],"promising":[2],"to":[3,44,54,84,110,118,141,158],"solve":[4],"linear":[5,130,164],"inverse":[6,165],"problems":[7,166],"by":[8,63],"unfolding":[9],"iterative":[10,13,36],"algorithms":[11,30],"(e.g.,":[12],"shrinkage":[14],"thresholding":[15],"algorithm":[16,107],"(ISTA))":[17],"as":[18],"deep":[19],"neural":[20],"networks":[21],"(DNNs)":[22],"with":[23,38,57,69,126,167,181],"learnable":[24],"parameters.":[25],"However,":[26],"existing":[27],"ISTA-based":[28,151],"unfolded":[29,152],"restrict":[31],"the":[32,39,86,98,104,139,178,187],"network":[33,74],"architectures":[34],"for":[35,162],"updates":[37],"partial":[40],"weight":[41],"coupling":[42],"structure":[43],"guarantee":[45,128],"convergence.":[46,79,131],"In":[47],"this":[48,136],"paper,":[49],"we":[50],"propose":[51],"hybrid":[52,106,174],"ISTA":[53,56,92,175],"unfold":[55],"both":[58],"pre-computed":[59,94],"and":[60,72,88,192],"learned":[61,114,124],"parameters":[62,125],"incorporating":[64],"free-form":[65,148],"DNNs":[66,68,149,161],"(i.e.,":[67],"arbitrary":[70,160],"feasible":[71],"reasonable":[73],"architectures),":[75],"while":[76],"ensuring":[77],"theoretical":[78],"We":[80],"first":[81,140],"develop":[82],"HCISTA":[83],"improve":[85],"efficiency":[87],"flexibility":[89],"of":[90,113,123,129,189],"classical":[91],"(with":[93],"parameters)":[95],"without":[96],"compromising":[97],"convergence":[99,168,184],"rate":[100,185],"in":[101,150,186],"theory.":[102],"Furthermore,":[103],"DNN-based":[105],"generalized":[109],"popular":[111],"variants":[112],"ISTA,":[115],"dubbed":[116],"HLISTA,":[117],"enable":[119],"a":[120,127,143],"free":[121],"architecture":[122],"To":[132],"our":[133],"best":[134],"knowledge,":[135],"paper":[137],"provide":[142],"convergence-provable":[144],"framework":[145,155],"that":[146,173],"enables":[147],"algorithms.":[153],"This":[154],"general":[157],"endow":[159],"solving":[163],"guarantees.":[169],"Extensive":[170],"experiments":[171],"demonstrate":[172],"can":[176],"reduce":[177],"reconstruction":[179],"error":[180],"an":[182],"improved":[183],"tasks":[188],"sparse":[190],"recovery":[191],"compressive":[193],"sensing.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-10T00:00:00"}